Music theory and the JoCoeuvre

Somewhat tabs-related, and I figure that the people who have the "JoCo Tabs" category blocked (which you, dear reader, can do by hitting the "Categories" tab and selecting "Block category") aren't significantly more likely to want to see music theory discussion.

As I've more or less said before, I am appreciative of music theory when demonstrated by others but too dead-eared to work it out myself. I'd do the whole link dump thing I usually do here where I find all the old threads where I expressed similar opinions, but I don't think anyone clicks my links anyway -- I'll eventually add a couple of previous threads where we discussed theory stuff shortly.

Briefly, this thread in particular is inspired by SpaceParanoids's inspired post about the craftsmanship behind "Shop Vac" (in the Favorite Song Tourney Matchup #16 thread). I'll quote the entire body of the comment, removing song-tourney-specific bits:

Shop Vac kicks off with the peppy 2-bar intro -- a simple phrase that will later be echoed by the background vocals during the chorus. These eight beats set the tone for the entire piece. The verse that follows jumps in on the V chord, which is a little unexpected from a Coulton composition. A steady, purposeful rhythm carries you through the verse... V, I, V, I... then builds with a familiar V, #vo, vi progression, before pausing on a suspended #vi that just aches to be resolved. The next two bars mellow out with a IVmaj7, which resolves to the minor-7th chord (a signature Coulton maneuver). The build into the chorus is nothing short of brilliant. The bass and guitar parts walk along the inspired I, III7, vi, IV progression while the melody weaves a perfectly balanced phrase around the instrumentation. The final build into the chorus recalls the augmented chord used earlier in the verse, and the entire package is wrapped up with a tidy ii7, V7.

The chorus that follows is pure pop bliss. The simplicity of the chord structure gives the layered vocals room to flourish, while the syncopated clapping punctuates each four-note phrase. Notice how the background vocals build a bridge between the two halves of the chorus. The second half reaches its satisfying coda with a fun little hop to the IV just before finally coming to rest on the I. After four beats you're right back into the driving rhythm of the V chord as the second verse takes off.

After the second chorus, you get to the bridge. We kick it off on the #V (yet another Coulton signature). I've always felt that the chorus sounded a bit thin. There's a little bit of empty space between the bass frequencies and the guitar appregio. And if I had one complaint about the song's structure over all, it would be that the bridge could be twice as long.

That structural gripe aside, the rest of the song is exquisitely constructed. In fact, Shop Vac is a masterpiece of power pop ennui...

I can read notation well enough to understand this, and I can read tabs though I'm not a guitarist, so immediately (still not in a position to listen to the song) I looked over at suuuupaadave's update to the tabs for "Shop Vac" (on JoCopedia here). Acknowledging, of course, that guitar tab notation is designed for ease of playing rather than for correctness under rules of music theory, I detect what I believe to be a couple incongruities (e.g. what SpaceParanoids terms a #vo chord, Dave has as G# = III, and I don't think it's the same under inversion).

If there's something to be fixed, tab-wise, I'd love to know (or fix it yourself on the wiki) -- that goes, too, for the error in the "My Monkey" chords that Paul et al. in the Mandelbrot Set seem to have found.

Anyway, nothing substantive from me on this subject, I just adore musical analyses like SpaceParanoids's (which I thought was brilliant), and I encourage more of them. I'm really looking forward to listening to the song again while paying attention to the things he points out.

Comments

Yeah I think I made an error. It probably is a G# chord. It may not even be inverted. It's hard to hear whether the bass note is a C or a G#. (Edit: It is inverted. The source track reveals that the bass note is a C.)

At any rate, I don't think I hear a Bbb (aka A) in there, so calling it a diminished seventh is wrong. A diminished triad would work, but at that point you might as well call it an inverted G#7, which is probably how it was written.

The final chord in that phrase is a little ambiguous as well. I was thinking of it as some kind of D6add2, but it's probably just a E7.

Disclaimer: I have no training in music whatsoever, so everything I know about theory I just kinda picked up along the way.

My tabs are mostly what the rhythm guitar plays and don't reflect the overall tonality. I do base a lot off of live performances and try to be as specific as possible. The lead sheets that colleenky and several others have done really are much closer to what the actual chords are in reference to all of the instruments. I'm glad that everyone's thinking and discussing these things though. I love being able to have a conversation with someone about all of the great geeky musical nuances I love so much.

Lotsa posts in the ShopVac thread were TLDR, so thanks to Bry for singling this one out.

Neat point of similarity between DNA and ShopVac - they are both unusual in starting off the verse on the dominant (V) chord, instead of the tonic (I). That weakens the tonality, and it really bugged me for the longest time, and still feels rather odd. In DNA, the whole first part of the verse is nothing more than an extended V chord (with a brief IV between lines).

Minor pedantic point of theoretical technicality, re the ShopVac bridge starting on #V... Technically, shouldn't this be called bVI? I know they're enharmonic, but the musical "spelling" seems more natural that way to me. By way of example, if you were playing in the key of C, it's more natural to say that you switched to Ab, which is Ab-C-Eb (and thus preserves the original C) instead of saying that you switched to G#, which is spelled G#-B#-D#. On the other hand, during the walk-up I would consider the bass note to be a #V (especially if the chord is an inverted III7 instead of an augmented chord), since here it acts as a leading tone. In the key of C, it would be the G# of an E major chord, acting as the dominant of A minor.

I've only got a basic knowledge of music theory (working on improving it as I find it very interesting), but I do know that sometimes it's quite ambiguous what a chord actually is. Especially when you start sticking extra notes in it and inverting things, and you've got a lot of movement through keys.

But I've got a lot more to learn about chords. Not playing any instruments which can actually produce them means my working knowledge of what various chords sound like is pretty low.

VI = C#, so bVI = (C#)b = C natural. So Bry is correct. Also, the chord C-E-G is related to the original key of E because of the shared note E, whereas Dbb would be spelled Dbb-Fb-Abb -- which is just gross.

I don't think Dbb can show up in the key E (at least not very easily)D# => Major 7thD#b => D => Minor 7thD#bb => Db => Diminshed 7th??? What interval is less than diminished?

I believe it's called double diminished. I doubt it has much use outside the crazy confines of modern experimental music though, since if you try to write it down in any way that looks like a double diminished interval instead of a less-diminished smaller interval, the musicians will hunt you down and kill you.

For what it's worth, pragmatism sometimes just has to win. Often I've found myself writing e.g. C instead of Dbb where the latter would have been theoretically correct. Why? Well, say it's the night before a 10am rehearsal for a show that night, and you just want to finish the damn arrangement. If the trumpet player screws up in the rehearsal and/or show, does it matter whose fault it was? When writing for transposing instruments, the issue can get pretty hairy, especially for alto sax and the like, where "easy" keys chosen for other players or a singer turn into horrible keys when transposed up a major 6th. This can be fixed sensitively by a human copyist, or steamrollered by a notation package that does the unreadable but theoretically correct thing.

On a vaguely related note (ha!), chord symbols and their interpretation are also tightly coupled to the culture in which they are used.The important thing is to do the right thing within your culture. Maybe the easy way out (relativism and postmodernism blah blah blah) but it works in real life.

Dammit. I was gonna make a quick comment and read the thread more thoroughly later, but Miss Pedantic Pants wouldn't let me. Now I've been sucked in. Thank a lot, Bry! ;-)

I'll be back....

ETA: I posted an edit and then realized I was just repeating what y'all had said. Yes, bVI. Yes, the sixth scale degree is C#, which flats to C. Dbb doesn't live in the key of E. It could be done, I suppose, but that would be pretty far afield, harmonically speaking. (Maybe it lives in the key of S. ;-) )

EATA: Double-diminished intervals? I don't think they exist! ;-) FWIW, Wikipedia tells me that they technically exist, but in practice, they might as well not exist.

P.S. I kinda wish sometimes that the tabs were done in Roman numerals instead of specific chords because a) it's easy to transpose, and b) it's easier to understand the harmonic movement. But that's just me. I understand that this is not The Way of Things. :-)

The problem with Roman numerals or Nashville numbering is this: sometimes things just break down when you get harmonically far afield from your home key. Simply stating chord names (using whichever convention you're comfortable with) means you're not analyzing anything except individual chords without worrying about context. Once you start referring to a home key, it gets more contentious, since you have another potential axis of disagreement: Just when do you consider the home key to have shifted?

Not that I suggest those two systems have anything inherently wrong with them; it's just that they require more buy-in in terms of an agreed grammar. Chord symbols alone don't go beyond spelling issues.

@Colleenky: While I agree that Roman numerals would be great (my above argument notwithstanding), I must admit that they'd require me to use my zombie-eaten brain a lot more!

I know, I know. That's just the way my mind works. I'm a tonal kind of gal. (When I transpose at the piano, I'm mapping scale degrees and Roman numerals.) I have to say, I enjoy plunking out the tabs on the piano, because then I have little "Hey, JoCo, I see what you did there" moments. I should do it more often. :-)

P.S. Granted, I only skimmed, but Nashville numbering looks a lot like a diatonic version of Roman numerals, using Arabic numerals.

Disclaimer: I have no training in music whatsoever, so everything I know about theory I just kinda picked up along the way.

I find that quote very interesting on many levels, SpaceParanoids. When I first heard your playing, I pegged you as somebody with a classical background, which I guess implies exposure to theory. Was I wrong on two counts?

And then there is the question of just what to make of the statement. My suspicion is that your theoretical mental model meshes 99% with a typical "trained" musician's, and of course one has to remember that different kinds of training produce different ways of thinking anyway.

Footnote: The notion that anybody can dare to use the phrase "a typical trained musician" deserved a thread of its own...

Colleen: I'm very similar, except that sometimes instead of mapping to Roman numerals, I mess myself up, and just map to the key of C. "Oh, C# minor in the key of E? That's just like an A minor... I mean vi." I even did that earlier in this thread. I can think both ways, but sometimes it's hard to control which way I'm thinking. I do the same thing listening to music... "Ok, I don't know what key I'm actually listening to, but that's a dominant (V), so it would be like a G chord."

I'm still not very good at doing either mapping in keys I'm not very comfortable with -- i.e. more than 2 flats or 3 sharps. Unfortunately, a majority of hymns in our hymnal have 2 or more flats.

I know I should be ignoring this thread, but I can't stay away. I just want to say that the fact that Bry apparently understands this thread after having done one semester of music theory in high school, and SpaceParanoids understands it with no music training whatsoever, makes me hopeful that maybe it is possible for me to catch up, somehow.

I did actually make some educated guesses about what some of these words mean while I was playing around with my keyboard the other week, and I was very excited about it, because my guesses were logically consistent, and consistent with everything I could remember people saying around here, but I haven't dared check to see whether they were right yet. I have a strong suspicion that you're just doing maths and hiding it behind (or 'making it accessible to non-mathematicians by using') fancy words (people always told me that maths and music were related, but my guesses show just how and how much. It's group theory, isn't it?) Can anybody recommend an introduction to music theory for mathematicians?

Angelastic: Yes, I do believe music and group theory are related, though I should be careful saying that, because my math training never quite went in that direction. But what your talking about seems to be related to Music Set Theory, which wikipedia admits is actually more similar to group theory. Unfortunately, that theory deals more with non-tonal music (IMO, yuck!), than with tonal, although some similar concepts apply.

For example, all pitches that are multiples of an octave apart (for example, all C's) form an equivalence class. Since an octave is 12 half steps, musical math uses modulo 12 -- like a clock face.

Any major scale can be represented by the tuple <0,2,4,5,7,9,11> which represents the number of half steps to go up from the starting pitch. That starting pitch is the key that you're in. In music theory, interval names are assigned as if these pitches were an array indexed starting at 1, so an interval of a fifth is the fifth element of that tuple, or 7 semitones.

A major chord is a tuple consisting of the pattern <0,4,7>. You can move that pattern of half steps to any starting pitch and get a major chord. If you start on the first note of the scale, you get a I chord, <0,4,7>, or C-E-G in the key of C. If you start on the fourth (5 half steps higher), you get the IV chord <5,5+4,5+7> mod 12 = <5,9,0>, or F-A-C in the key of C. Similarly, starting on the fifth, gives the V chord <7,11,2>. These are the only major chords that exist in the major scale, and explains why I-IV-V chords are so common in music. (if you try using the major chord pattern with any other notes in the scale, you'll get notes that aren't in the scale, e.g. if you start on 2, you get <2,6,9>, but 6 isn't in the major scale).

I don't know if that helps, or just confuses you. Most of the places where music is taught like this, they assume some amount of previous music theory, and/or assume that you're interested in non-tonal music.

I don't know what the difference between tonal and non-tonal music is, but this seems interesting and quite understandable so far! Is there some reason why it goes from 4 to 5 rather than 4 to 6, and then continues going up by twos as if nothing had happened? Does it sound better that way? Is it just so that you can have seven notes without getting to 12 (which would be the same as 0; and that part I completely understand because I not only know modular arithmetic but I also read Euler's explanation of music and I specifically remember this stuff about ratios of frequencies ETA: I'm starting to think that if I reread that then it would even answer this question, but unfortunately I lent the book to a friend, so I'll have to find it online some time when I'm not supposed to be working)? Is this little kink the thing which makes it difficult to transpose (I don't know whether I'm using that word correctly) between keys (or that one), and which makes it so that (as my friend told me after I had misread Colleenky's transcription of Still Alive) what looks for all the world like a C is actually supposed to be a C# because of the key it's in?

There actually is a scale that continues by two's <0,2,4,6,8,10>, and it's called the whole tone scale. It has a mysterious, otherworldly, sound -- used a lot in sci-fi, I think. The problem is that it's so uniform, that there's no easy way the ear to define a stable point of reference. It's a bit like Escher's staircase. The asymmetries between 4 and 5 and between 11 and 12 give a scale it's "character" (non-mathematical term, I know!).

You're also right to assume that the ratios in frequencies come into play. The fourth and the fifth (5 and 7 semitones) sound very pleasing to the ear (think of the interval between P&S in Nun Fight -- that's a fifth) because their frequencies are *ideally* small integer ratios of each other. On the other hand, 6 semitones (called a tritone, or a diminished fifth (7-1=6) or an augmented fourth (5+1=6)) is considered to sound unstable, and hard to sing. In medieval times it was even considered diabolical.

I said *ideally* about the ratios, because the majority of music today uses a tuning system called "equal tempered" which slightly messes up all the frequency ratios in order to get a completely relative system that can work in every key. This is a topic that gets really confusing for me, and most musicians never think about it anyway (unless you're playing early music, or tuning a harpsichord) so I won't go into it now. Suffice to say that the main problem is that the fractions created by frequency ratios don't correspond perfectly to a logarithmic scale.

To those who are looking to improve their music theory knowledge I can recommend this book.It's really good and easy to understand. It's also practically the only music theory instruction i've ever had.

Is this little kink the thing which makes it difficult to transpose (I don't know whether I'm using that word correctly) between keys (or that one), and which makes it so that (as my friend told me after I had misread Colleenky's transcription of Still Alive) what looks for all the world like a C is actually supposed to be a C# because of the key it's in?

I think you're talking about the key signature, which isn't quite the same -- it's used as a kind of shorthand.

To relate it to what voidptr said above, an octave (from C to C, for instance) is divided into 12 half steps but only 7 of those 12 notes are used in a major scale. For instance, in D major, C# (11 half-steps up from D) occurs in the major scale, but C natural (10 half-steps up) doesn't. That means that a piece that's in D major won't typically (I'm simplifying) use C natural -- instead it'll use C#. So the key signature just tells the reader, "You're in D major, so all the C's, unless otherwise specified, are really C#'s."

[Of course, using notes that aren't in the stated key, like C natural in D major, is hardly uncommon, but the key signature tells you what the defaults are.]

@voidptr: Thanks for that fantastic bit of set theory. I have never really explored that much, but you have obviously given it some thought, so please do elaborate more. If we were purists, somebody would say something like "Where's JoCo in all of this?" (too) soon, but I am confident that things will link up in due course.

@Angelastic: I like you angle about hiding things behind terminology, but I think it is more akin to natural language than to maths. Our spoken and written English tends to be way better than it would have been to if we were only allowed to use constructs that we have the vocabulary to analyse. [Extra points: Explain what is wrong with that previous sentence ;-)]

@both: Ever thought of key modulation in terms of a call stack? There's an Edsger Dijkstra parallel waiting in there somewhere.

ETA: Why stick with stack frames? How about chromatic notes and variable scope?

I'm dying to find out what key modulation is now, so I can think of it in terms of a call stack, but I'll wait till I get home. In the mean time, my subconscious will come up with hypotheses about things in music which are like call stacks.

Oh, wait! This is like that chapter of GEB where they're jumping from one nested world/dream/description (I forget exactly what) to another and then they don't actually get all the way back out to reality at the end of the story, which would correspond to going back to the original key or whatever it is in music, which is called the tonic, and is somehow pleasing to the ear to get back to! I know what you mean! I mean, I still don't really know what key modulation is, but I know how it's like a call stack! I need to read that book again. (In French, for a change of... timbre, and some other musical thing which is less straightforward to change?) Quick, before the next issue of New Scientist arrives!

You got me excited again. Stop doing that when I'm trying to work.

First thing wrong with the sentence: missing 'r' in 'your'. Second thing, it's distracting me from what I'm supposed to be doing.

While you all are geeking out over music theory, a subject near and dear to my heart but which I am sadly pretty weak at applying, would anyone like to give a listen to JoCo's electric guitar part for "My Monkey?"

The tab is wrong, and I did not realize it was wrong before recording it for the Mandelbrot Set. I'd like to record it with guitar voicings that are closer to the original, but I'm not all that good at hearing tones. There are some 7ths or major 7th or other tones in there that the tab doesn't capture. It would also be nice if the tab named the chords, although given that it is finger-picked they are mostly partial and altered chords.

(Yes, I am trying to get other people to help me with what is really my job as a guitar player, but at least I admit it. I'm also wondering whether, musically, it is really necessary to get the 7ths and other color-alterations right in the guitar part. Maybe I don't need to bother?)

@Paul: Any particular part in the song (mm:ss or verse x) that cause problems? I can't help with tabs, but I should be able to add an opinion to naming chord symbols, not to mention starting an argument over which naming convention to use! Which set of tabs are you comparing with?

You could think of key modulation as a call stack - push a new key on, pop it off later, eventually return to the home key when the stack's empty at the end of a piece - but I think that would be unwise in the general case. Does a symphony, which would often have a sort of journey through various keys to reach the home key, have a completely symmetrical key structure?

However, it should be remembered that almost all music will return to the home key (the home key almost always being the key it started in) at the end, which gives you an audible clue that it is the end. If you end in a different key, it can feel unfinished.

An exception to that, of course, would be pop songs with a key change at the end, which are quite likely to finish in their new key. That works because they establish the new key firmly enough that you accept it as the home key by the time it lands on what is probably going to be a strong perfect cadence in that key (a perfect cadence is the dominant chord, which is chord V, followed by the tonic chord, which is chord I - neither of which is inverted. It gives a very strong sense of ending, and an awful lot of music has a perfect cadence at the end and possibly at the end of significant sections in the middle).

Now I'm babbling. Damn.

I really do recommend playing with these things on a keyboard or piano (something I can't do very easily as I don't have a keyboard yet). Take C major, play the tonic chord I, then maybe play chord IV, then finish with V and I. You can do quite a lot with a I-IV-V-I progression, although it isn't anything at all surprising and might be considered boring. You'll hear how the V chord feels incomplete, how you want to go somewhere else with it, and how the I chord completes it. For a stronger sense, add the seventh to the V chord, which makes it feel even more like it wants to resolve to the tonic.

Another common cadence is IV-I, called the plagal cadence. It's weaker than a perfect cadence, but still turns up at the end of a fair few things - one reason being that IV and I both have the tonic (the first note of the current key's scale) in, so it fits nicely with a melody that repeats that note through the end. The name comes from its common use to go with the two syllables of "amen" at the end of church music.

Needless to say, there are also other common ones which land on other chords, and other ways to get to chord I.

I now babble excessively, so I shall stop. Music theory is fun, isn't it?

Borba: the part is maybe not so audible in the finished mix as it is in the un-mixed tracks. The tab is the one in the MP3 store (http://www.jonathancoulton.com/songdetails/My%20Monkey).

There are really only a couple of phrases: a repeating phrase that plays under "my monkey gets ... sometimes," an alteration of that as it leads into the verse chords, some chorus chords. The tab mentioned above has them as pretty much major, minor, altered to sus 2, which doesn't actually sound right.

I really do recommend playing with these things on a keyboard or piano (something I can't do very easily as I don't have a keyboard yet). Take C major, play the tonic chord I, then maybe play chord IV, then finish with V and I. You can do quite a lot with a I-IV-V-I progression

Ooh, I have a keyboard! I'm going to go home now and see if I can figure out what those chords are and how to play them. And if at first I don't succeed, I'll eat some dinner.

I just tried it. Nothing at all surprising happened, so I must have done it properly. I discovered my fingers aren't very stretchy, though. Also, Louie Louie didn't bring me any fame, but it stopped me from asking a stupid question.

With my newfound musical skill, I will... um... well, maybe I should go to bed, really. Nah, I'll learn to play one of the tunes I've made up over the last few months, so that I'll have a record of it in case I forget.

ETA: I just noticed that if I play G, A, B (not chords, just single notes) it also sounds quite similar to Louie Louie, just not as cool-sounding. Is there some deep music-theoretical reason for this or am I just tone deaf?

@Paul: I had a listen to the recording, and here's my admittedly subjective take on it. Caveat emptor: as expected, this goes into interpretation territory!

Using the intro as the lazy man's model for the accompaniment (please point out if you believe this to be bad choice) I would notate the first phrase simply as four chords: E B C#m A. These give the essential character of what you hear, and adding anything else to the notation will mean that somebody playing from nothing but the chord symbol will probably play something strange-sounding instead of converging on JoCo's performance. If we want to be more fine-grained, I'll concede the following detail:

The B does get a prominent 7th on the second half of its beat. Maybe you could notate it as B going to B7. Strikingly, it lacks a 5th (F#), turning the B+A dyad on the second beat into a stronger statement.

The accompaniment pattern on the C#m passes through D# to E on the highest note (B-string?). If this were taken to be a harmony note, it would suggest that the chord is actually a C#m9, a reading which is reinforced by the bass passing through B on its way from chord root C# to the next root A; this B would be the otherwise missing 7th in the minor 9th chord. However, both these notes have valid non-harmonic alibis for being there: accented and unaccented passing notes respectively. [MaW, voidptr or Colleenky might catch me out on a small point here, extra credit for correcting me!],

A is really just a plain triad, although the very last eighth note is a "passing" B, which I perceive as an anticipation of the next chord's 5th - I don't hear it as an added 2nd/9th. [ETA: given how I brought the vocal line into play below, I should point out that the vocal adds a major 7th on "some-TIMES"]

Phrase 2 is pretty interesting in how it blurs the harmony, so we are moving further away from simple chord symbols. Although one can cut it more subtly that this, I propose the following rough reading:

Functionally, the first chord is just an A triad, and the main vocal line supports that up to just before the chord change - nothing contradicts A if you just look at the bass note and the moving vocal line.

The second chord is problematic in terms of filling in the question marks between the bass note B and the melody notes E->G#. The melody suggests an E major chord, which would actually have worked as a slightly lame alternative harmonisation. Seen from another angle, the B chord would have worked "cleanly" if the melody notes were D#->F# instead. If the bass note and two melody notes were the only given, I would have said it would harmonize as an E major second inversion (E/B).

Back in the real world, JoCo decided to harmonize the second chord as a type of B, catachresis be damned. If the given now is that we have a B major triad with the notes E and G# as melody on top, you now have a few options. Without the E, it would have been heard as a 13th chord, but the E (perfect 11th) jars with that reading, since a 13th would normally have either no 11th or a raised 11th, and anyway it would suggest a "jazzy" feel which is not in keeping with the song's style. One could explain the E away as a temporary "suspension", but that just begs the question of resolution, and there is really nowhere it resolves to. I'll leave that though suspended for the moment, as it were.

The secondary vocal line gives us an interesting clue though: it is consistently a diatonic third above the main one. Seen in isolation, the combination of the two vocal parts suggest three chord changes: "cause every"(E) going to "monkey needs a"(A) going back to "long time"(E). Together with the bass and parts of the guitar chord, the total sonority for these three chords is something like (E major above A major) -> (A major) -> (E major above B major)

At this point one may rightly ask what is the difference between a A major triad with an E major triad on top and an Ama9 chord. I have to shrug and say it's how you feel about it.

To get somewhere towards a quick answer to the original question about the second phrase:

Given that the A chord does eventually feature a G# in the guitar, and that the E+G# sonority occurs in the vocals, you could label it as an Ama7. Alternatively, E/A would do nicely, and if the air guitarist in me isn't mistaken, can easily be voiced with a single finger (skipping the open low E and D strings, with the first fret on the G string)

The B chord is difficult to pin down to a symbol. My best guess as to a plausible voicing to capture the essense of the recording (assuming you've got a vocalist singing the main line) is to try a B7, omitting the 5th. This is just instinct speaking, but I'd be interested to hear if it works for you.

@Mark: I doubt if he would do what I did above, for the simple reason that it's a combination of after-the-fact justification and forensic work. Maybe he does it with other people's songs? I should point out that the "analysis" above hardly touches upon analysing the song as such; it's simply some stream-of-consciousness musing upon a few very small aspects of it. I suck at coherent analysis and bigger picture stuff!

ETA: Then again, I gladly grant him the right to analyze as much as he wants. One persistent problem that afflicts artistic folks is that others are happy to ascribe God-given talent to them, but deny them the right to be respected for hard work and study. In its crudest form, it finds expression in the charming colonial notion of "Ah, those natives are such Natural Musicians," i.e. they didn't do anything to achieve their skill level. On the other hand, some people are really just born with too much talent ;-)

EATA: Wait, I think the canonical version of the above quote is "Those natives are born musicians - such natural rhythm!"

Borba: thanks for the detailed notes! Haha. that was a little pune or play on words.

I have a little quiet time tonight before I have to collapse, so I'm listening/playing. Your notes have given me some insight into what to listen for.

It sounds to me like the first phrase goes:

E major (played in open position; the 5th string is skipped)

I now think the second chord is not a B at all, but is actually fingered 0 2 1 2 0 0. This makes it a B/D#/A triad which I'd call -- a B7sus4 fingering I've never seen before? I know a triad doesn't make a tetrachord but it seems to imply one here (and on guitar, you often drop notes from chords to meet the actual demands of available fingerings).

I think we're in agreement that the 3rd and 4th chords are fingered the C#sus2 altered to C#m, and A altered to Asus2.

On the changeover into the second phrase, there's an alteration: instead of jumping down to the A, there's a straight B major triad interjected.

The phrase with the repeating A: ah, there is something altered here. I think h4wk pointed out that this is an Amaj7, and then the B is that same altered chord with addition of the F# note on the high E string.

Here's how I'm tabbing it now. First, the fingerings (note that not all the notes are sounded)

These are finger-picked and not strummed in full and in some cases the chords are suggested only by one altered note hammered-on or pulled-off. Maybe I'll try to tab out the whole thing.

Figure 1:
E B7sus4 C#sus2 C#m A Asus2

Last repeat each verse:
E B7sus4 C#m B

Figure 2: (note: the timing varies)
Amaj7 B7sus4

Last repeat each chorus:
Amaj7 B7sus4 (end on picked F# single note on 1st string)

Last chorus ending:
Amaj7 B7sus4
Amaj7 B7sus4
E (pick notes slowly)

Let me play that through a few times and see if I hear any further tweaks to make. Then maybe I will re-record the line like that. Looks like I will also need to revise my little video: http://www.youtube.com/watch?v=orXk2KIZXwo Serves me right for believing tab without working it through note-for-note myself.

That Amaj7 B7sus4 (or however you spell it) is really clever -- same fingering shape, totally complimentary tonality, especially when bringing in the F# leading tone. Given the way these chord shapes fit together, I would bet that JoCo composed this part on guitar, by ear, without giving a whole lot of thought to analyzing the harmony. I know he did study theory, which has certainly educated his ear, but I just don't think that's how he rolls, as he puts it. I'm starting to wonder if he writes out any parts at all when he's composing, even chord names? In any case, learning how he plays all these guitar lines has been quite an education... that's what keeps bringing me back to it. Then getting them down well enough to record -- that's a whole next-level of challenge that I've been really enjoying!

@Paul: I'd agree that it was composed on guitar. The biggest open question is whether the accompaniment pattern or the song proper came first; I suspect they could plausibly have led separate lives at first, and then met on a lucky night. And I'd also suspect that JoCo doesn't need to write out chords. If he couldn't remember the My Monkey chords while composing, he has a problem ;-) On the other hand, having noodled up the accompaniment, one wouldn't want to forget it, so possibly a little audio recording would serve. Writing either notation or tab would be too slow and distract from the creative flow, unless he has incredible concentration.

Regarding B7sus4, the one problem with naming a chord as sus4 is that it implies a missing 3rd. I'd probably label it B7add4 if both the 3rd and 4th are present.

I have a little idea fermenting now; stirring up analysis (or more) by presenting snippets of alternative takes on JoCo songs. Could be a good use for the stranger things that happen when I noodle the songs on piano.

I don't know what the difference between tonal and non-tonal music is, but this seems interesting and quite understandable so far! Is there some reason why it goes from 4 to 5 rather than 4 to 6, and then continues going up by twos as if nothing had happened? Does it sound better that way?

It's not a matter of "better," that's just the definition of a major scale. You know that two half steps (or semitones) make up a whole step (or whole tone), yes? A major scale is made up of two tetrachords (four-note sets) separated by a whole step, where the interval pattern of each tetrachord is whole-whole-half. This is pretty cool, because it means you can create a new major scale by stacking a different tetrachord a whole step above or below the previous one. If you start on C and play eight notes up on just the white notes of the piano, you end up with:

This is where key signatures come in. Let's say you want to play a major scale starting on G. The tetrachord a whole step above the G tetrachord would be D E F# G. which means that to get the "major" pattern, you need to play an F# instead of an F. Rather than putting a sharp by every blasted F in the piece, just sharp the F once at the beginning and be done with it. (We musicians are lazy people, always looking for shortcuts.) And yes, you can creat different kinds of scales by using different patterns of whole and/or half steps. Voidptr already referred to the whole-tone scale. There's also the chromatic scale, which is all half steps. And there are the modes, which you can discover by playing octave scales on the white notes of the piano (D to D, E to E, etc.).

The pattern of the key signatures is called the "circle of fifths." As you add sharps, the tonic shifts up by an interval of a fifth. As you add flats, the tonic shifts down by a fifth. (FYI, fifths and fourths are inversions of each other. G is a fifth up from C, but also a fourth down. Any two intervals that add up to nine are inversions of each other.)

To add to the fun, the order of the sharps (F C G D A E , is the reverse of the order of the flats (B E A D G C F). Also, the last sharp in a key signature is always the seventh pitch in the scale, while the second to last flat in a key signature is the name of the key.

Speaking of the circle of fifths, note that in the C major scale above, the starting pitch of the second tetrachord is a fifth above the tonic. This speaks to why the I IV V chord progression is so fundamental! V is based on the tetrachord above tonic; IV is based on the tetrachord below tonic (F G A Bb). V is called the "dominant," and IV is the "subdominant." And since the I chord is a fifth above the IV chord, I is the dominant of IV. The fifth is pretty much the basis of Western harmony. The closer one stays to these fundamental relationships, the more logical and "pleasing" the music. The farther afield, the more strange. Jumping to a completely unrelated chord tends to sound extremely jarring.

A modulation is when you change keys during the course of a piece. The casual term is "key change." Very original, no? A piece may have one key change or several. If a piece changes keys for just a short period of time, it might not be termed a modulation. Instead, it could just be "borrowing" chords from another key. Modulation vs. borrowing can be pretty subjective. There is no hard and fast rule to determine how much borrowing constitutes a bona fide modulation.

Finally, "tonal" music is written using the set of pitches from a given key and, possibly, related keys. In "non-tonal" or "atonal" music, some other method is used to determine the set of pitches (mathematical, random, etc.). Atonal music tends to sound chaotic in comparison to tonal music. Atonal music was meant to be studied and not necessarily heard. That's not a snark; that's just a fact.

Whew! Any questions?

ETA: @MaW: As I understand it, "sus4" means that you play a 4th instead of the 3rd. B7sus4 = B E F# A.

I'll start with one question, and then a whole lot of rambling about what I didn't understand until a few weeks ago when I thought I had figured it out, and that now has some relationship to what you're actually saying, and might be more or less correct.

Wait wait wait, you say that E to F and B to C are half-steps? Why?

I think the main thing that has tripped me up in all this, ever since I first attempted to read web pages about music theory, was this idea, which seems to be very important, that a piece is written in a certain 'key' (or scale?), and there are all these keys with different names, but... why? I figured out that a key is basically a set of notes (yay, you said that in your last paragraph, I was right!) but there are so many of them, and it seems like you are allowed to use the occasional note which isn't in that set, and change key part-way through a piece. So it seems like you could just write some music, and then figure out which notes are in it, and work out the key from that (which you say is atonal! I learnt something!) and I don't really see what the point would be of figuring that out. And how can you even tell when the key changes? I am sure that there would be some notes which are in both keys so there's no definite point where it changes. Ooh, but that's the whole modulation vs. borrowing thing, which you mentioned. So I was right to wonder about that.

But there must be some advantage to picking the set of notes before you start making music with it, so I guessed that these are sets of notes in which a certain relationship that holds between the notes (which I think you confirmed in your first paragraph), such that things written with just these notes sound particularly good (which maybe you denied in the first paragraph, but confirmed in the last paragraph.) So, like, these sets are all isomorphic to each other or something. And if you play the same song in different keys (where these same relationships between the notes hold) it still sounds like the same song, almost as much as if you played it in another octave. And I'd heard of major and minor keys, so I figured that minor keys are sets of notes where a different (but still the same for all minor keys) relationship holds between the notes in the set, which sounds good in a different way. And one of the different things is that one or the other of these (major or minor, I forget which) sounds sad to people from most Western cultures, while the other one sounds sad to people from other cultures, because actually, there's no universal inherent emotion in music. But I wonder who would find 'Mr. Fancy Pants' depressing.

To reply to a mention of me above, my training in music theory is only that one semester I mentioned, but I've mentioned in the past my having played (and I quote) "[a]bout five years piano, a little violin ('to play the world's saddest song'), while growing up -- haven't played either seriously in ages".

Wait wait wait, you say that E to F and B to C are half-steps? Why?

To back up a little: The white keys on the piano keyboard, and the letters that correspond to their notes, are the notes that make up the C major scale (not going into history of the keyboard / note names right now, although by request I could actually do research). And as you know, the C major scale, like all major scales, comprises 5 whole steps and 2 half steps, in the familiar WWHWWWH pattern.So perforce, if the white keys make up the C major scale and there are two half steps in the C major scale, then there must be two pairs of white keys that have no "note" in between them. (Let's continue not to talk microtonalities and other "modern" affectations.)

The WWHWWWH pattern also, as you see, determines where the black keys fall -- a whole step is two half steps, so the whole step between C and D is made up of two half steps, C-C# and C#-D. So the pattern of the black keys (Angelastic will appreciate the notation "1 for a key, 0 for none": 1101110) corresponds to the pattern of the major scale.

I always wondered about the gaps in the black keys. So... but... um... does this mean that... oh, never mind. I'm going to spend the rest of the day mourning lost notes and the fact that the only explanation I understand from that thread is the one about making it easy to tell which note is which. I can understand that if you go up by half-notes here, and whole notes there, it some kind of nice-sounding scale... but then it turns out the notes themselves are named such that even by counting up by ones you are sometimes counting halves... so then you may as well just hide the whole WWHWWWH pattern behind that abstraction layer and forget it exists. Or is that what we do? Now I don't even know why it's called a half-step, because it's not half of anything except for two of itself. It's not even half the distance between two perfectly-normal-notes-without-sharps-or-flats.

Q: Why are the black keys black?A: They are mourning B# (by day, Cb by night!) and E# (nee Fb) (which don't exactly not exist, but go by the yet-more-secret identities of C amd F, if I am not mistaken, but it's still sad.)

Is the piano (and its keyboardy cousins) the only instrument that, um... folds up the sequence of notes such that the all-important C-major scale forms a convenient line of white (or otherwise obvious) things? Or do they all do it? Or does it depend on tuning? (This would be why I hear people talking about tuning a guitar in D-major or whatever it is I've heard people talking about. Hey! I think despite all appearances, I'm making some kind of progress here!)

There's a song I like where somebody is singing about how great girls are (he was 18 when he wrote it) and he says (in French, so it rhymes) that they're great like the black keys on a piano, and like the biggest slice of cake. Now I know why he put those two things together. They are both lies!

Sorry about this. Do go on discussing music theory and the JoCoeuvre. I'll be okay once I've had some chocolate. And probably once I have carefully reread everything people have told me. Which I will only do after the chocolate. Thanks for the help.

...a piece is written in a certain 'key' (or scale?), and there are all these keys with different names, but... why?

Great question! And I'd appreciate input from actual musically-minded people on my answer, which runs as follows:* First off, if you can find a "key" in the sense of "one of these twelve (or 24, if you count minors separately) sets of notes", it's not going to be atonal -- atonal music might use the notes within a specific set of notes, but as I understand it, if it's got a key, it's got tonality.

* But a key is just a set of notes that people think sound "better" with each other. You don't have to establish a "home key", but if you don't, you'll create some confusion or unease on the part of the listener. Sometimes this is intentional -- and sometimes disguising the home key or delaying the establishment of the home key can be an effective technique. For instance, if I were writing in the key of C, I might lead off not with the I chord but with some other chords (IV, vi, whatever), so that when I actually hit the I chord, it'd be more of a release of tension, more of a feeling of, "Oh, that's where I'm supposed to be!" (Musical in medias res, as it were.)

* Having a key before you start writing a piece makes it easier, among other things, to tell people how to play it. It's helpful, too, to give a sense of what you're working towards and where you want to return in the resolution.

And for every key, there are chords that sound better in it than others. The chord C-E-G is the I chord in C major, the IV in G major, and the V in F major, so it sounds "natural" in these keys. But in D major (and all the rest of the sharp keys), you'd expect C#, and in Bb major (and the rest of the flats), you'd expect Eb, so it's not really native to those. You could play it, but it'd be an ornamentation, rather than a normal part of the key.

* How do you know when you've moved from one key to the next? Well, largely a judgment call. If I just play you that C-E-G chord, you can't tell right away if I'm actually in C major or in F or in G or even in something else. Recall that G major is different from C in one note, the F#. If I don't play any F's or F#'s, you might not be able to say definitively that I'm in C and not in G, but there should be a sense of a home key (this will be easier to see when listening to specific songs).

But if you think that my home key is C and then I start throwing in F#'s, can you tell whether I've changed keys to G or whether I've just started decorating my song with notes outside the key? Not immediately, but based on the rest of the chords, you might start to feel as though the home key has changed. Or perhaps not! Maybe I've gone into another key for dramatic effect but the piece as a whole is still in C. That's largely a judgment call -- even in the classical period, where a lot of these rules flowered, a lot of pieces (I'm most familiar with Mozart sonatas, but they're hardly alone in this) include a part where the main theme gets repeated in a different "key". I put "key" in quotes because they're not usually marked with new key signatures, even though they could be. This more or less indicates that the overall home key is still the original key, even if the apparent home key in this section is something else. But if you wrote a new key signature here, you wouldn't really be "wrong".

* And to anticipate a related question: So if all these keys are isomorphic to one another, why choose one over another -- why write in C major and not in Ab major, or something? Well, some keys are easier or harder to play for some instruments -- strings prefer sharp keys, woodwinds and brasses (I'm given to understand) flats. Even on the piano, where you can play in any key you like, different keys have different feels to them to the expert listener, which you don't need to worry about too much at this point. This just has to do with how the piano is tuned / constructed -- white keys generally sound a little brighter, and I won't go into details because I'm not an expert myself.

* (I use "scale", by the way, to mean the specific arrangements of notes in order upwards or downwards -- C-D-E-F-G-A-B-C, for instance -- and "key" to mean the set of notes in a scale, which you can use in any order. This is probably lopping off a few dozen nuances, but no one seems to correct me when I do it.)